MurphyKate Montee

Education & Professional History

University of Notre Dame, BS; University of Cambridge, MASt; University of Chicago, MS

I got my PhD in 2020 from the University of Chicago. My advisor was Danny Calegari. I graduated with an MASt in Mathematics from Cambridge University in 2014, and a BS in Mathematics and Music (Vocal Performance) from Notre Dame in 2013.

I’m interested in geometric group theory, especially questions about random groups and cube complexes. The first papers I read in graduate school were by James Cannon: The Combinatorial Structure of Cocompact Discrete Hyperbolic Groups, and The Theory of Negatively Curved Spaces and Groups. While I read these in graduate school, they are accessible to any undergraduate familiar with groups. For any undergraduates interested in geometric group theory, I highly recommend them! For a more systematic approach to GGT, I also recommend the book Office Hours with a Geometric Group Theorist, edited by Matt Clay and Dan Margalit.

Here is a statement on my research, including potential projects with undergraduates.

Current Office Hours

I’m available by appointment via Zoom. Please use this link to sign up.

Past Courses

University of Chicago

• Instructor, Calculus and Elementary Functions I-II (MATH 13100-13200, Section 58) Spring and Winter, 2019 and 2020.
• Co-Facilitator and -Creator, Fundamentals of Teaching in the Mathematical Sciences, Fall 2019. These four 90-minute sessions are a chance for graduate students in the mathematical sciences to meet, discuss their teaching, and learn about current evidence-based approaches to improve learning in your students. Co-taught with Karl Schafer.
• Instructor, Linear Algebra (MATH 19620, Section 50), Fall 2018.
• Instructor, Number Theory, SESAME Program at University of Chicago, Spring 2018. Webpage here.
• Instructor, Harris School of Public Policy Math Camp, Summer 2017 (webpage here), Summer 2018 (webpage here), and Summer 2019 (webpage here).
• Instructor and Creator, How to Solve it, Fall 2017 and 2018.
• Grader, Graduate Algebraic Topology (D. Calegari), Fall 2016.
• College Fellow, Honors Calculus 161-163 (J. Stehnova), 2016-2017.

Undergraduate Mentoring

I have mentored several undergraduate students in independent reading/research projects, including the following:

• Chi Nguyen and Xingyi Zhang: Graphs with Many Hamiltonian Paths
• Erik Carlson and Will Fletcher: Hamiltonian paths in non-Hamiltonian Graphs
• Emily Gentles: Simple Random Walks
• Jake Koenig: Generating the mapping class group with Dehn twists
• Can Liu: Ramsey Theory
• Charlotte Rieder: Finitely generating the mapping class groups with Dehn twists
• Eric Silva: Riemannian Geometry and the Gauss-Bonnet Theorem
• Eric Silva: Solving the Word Problem in Hyperbolic Groups
• Mary Stelow: Hamiltonicity in Cayley graphs and digraphs of finite abelian groups
• Xingyu Wang: Random Groups and Hyperbolicity

Papers

• Random groups at density d<3/14 act non-trivially on a CAT(0) cube complex. [arXiv] To appear in Transactions of the AMS.
• Property (T) in k-gonal random groups. [arXiv] To appear in Glasgow Journal of Mathematics.
• Mathematics of the Fon people. With T Helke. Submitted.
• Knot projections with a single multi-crossing, with Colin Adams, Thomas Crawford, Benjamin DeMeo, Michael Landry, Alex Tong Lin, Seojung Park, Saraswathi Venkatesh, Farrah Yhee. Journal of Knot Theory and Its Ramifications. Volume 24 (3) 2015. [arXiv]

Papers with Students

• Graphs with Many Hamiltonian Paths. With Erik Carlson, Willem Fletcher, Chi Nguyen, Xingyi Zhang. [arXiv] Submitted.

Not for Publication

• Topic Proposal: Cubulated Groups
• Complementary regions of multi-crossing projections of knots. [arXiv]

Vocal Biography

MurphyKate Montee, soprano, lives in Northfield, MN. Her performance experience includes concert and chamber works, including the soprano solo in Haydn’s Missa in Angustiis and the role of Lieschen in Bach’s Coffee Cantata. In 2014, she performed the role of the Countess in Mozart’s The Marriage of Figaro in a concert setting, where she was lauded as “rich-voiced, impressive” (Sardines). She has also performed in dramatic settings, in stagings of Tobias and the Angel (Edna), Dialogues des Carmelites (Blanche de la Force), and Sweeney Todd (Mrs Lovett).

MurphyKate studied under Patrice Michaels while earning a PhD in Mathematics from the University of Chicago. In 2013, she graduated from the University of Notre Dame with a BS in Music, where she studied Vocal Performance with Mark Beudert.

MurphyKate’s Vocal CV can be seen here.